We appreciate your visit to What substitution should be used to rewrite tex 4x 4 21x 2 20 0 tex as a quadratic equation A tex u x 2 tex. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
To rewrite the equation
[tex]$$4x^4 - 21x^2 + 20 = 0$$[/tex]
as a quadratic equation, we first notice that the term [tex]$x^4$[/tex] can be expressed as [tex]$(x^2)^2$[/tex]. This observation suggests a substitution that simplifies the equation.
Step 1: Let
[tex]$$u = x^2.$$[/tex]
Step 2: Express [tex]$x^4$[/tex] in terms of [tex]$u$[/tex]. Since [tex]$x^4 = (x^2)^2$[/tex], we have
[tex]$$x^4 = u^2.$$[/tex]
Step 3: Substitute [tex]$u$[/tex] into the original equation. The equation becomes:
[tex]$$4u^2 - 21u + 20 = 0.$$[/tex]
This is now a quadratic equation in terms of [tex]$u$[/tex].
Thus, the substitution that should be used is:
[tex]$$u = x^2.$$[/tex]
[tex]$$4x^4 - 21x^2 + 20 = 0$$[/tex]
as a quadratic equation, we first notice that the term [tex]$x^4$[/tex] can be expressed as [tex]$(x^2)^2$[/tex]. This observation suggests a substitution that simplifies the equation.
Step 1: Let
[tex]$$u = x^2.$$[/tex]
Step 2: Express [tex]$x^4$[/tex] in terms of [tex]$u$[/tex]. Since [tex]$x^4 = (x^2)^2$[/tex], we have
[tex]$$x^4 = u^2.$$[/tex]
Step 3: Substitute [tex]$u$[/tex] into the original equation. The equation becomes:
[tex]$$4u^2 - 21u + 20 = 0.$$[/tex]
This is now a quadratic equation in terms of [tex]$u$[/tex].
Thus, the substitution that should be used is:
[tex]$$u = x^2.$$[/tex]
Thanks for taking the time to read What substitution should be used to rewrite tex 4x 4 21x 2 20 0 tex as a quadratic equation A tex u x 2 tex. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
